Nonsingular Morse–Smale Flows with Three Periodic Orbits on Orientable $3$-Manifolds

The topological equivalence of nonsingular Morse–Smale flows under assumptions of various generality has been considered in many works (see, e.g., [1]–[4]). However, in the case of a small number of periodic orbits, it is possible to significantly simplify the known invariants and, most importantly, bring the classification problem to implementation by describing the admissibility of the obtained invariants. In the recent paper [5], an exhaustive classification of flows with two orbits on any closed $n$-manifolds was obtained. The present paper gives a complete topological classification for flows with three periodic orbits on orientable $3$-manifolds.